Chapter 8. FAILURE

Introduction
Failure of materials may have huge costs. Causes included improper materials selection or processing, the improper design of components, and improper use.

Fundamentals of Fracture
Fracture is a form of failure where the material separates in pieces due to stress, at temperatures below the melting point. The fracture is termed ductile or brittle depending on whether the elongation is large or small.
Steps in fracture (response to stress):
track formation
track propagation
Ductile vs. brittle fracture

Ductile/ Brittle

deformation extensive/ little

track propagation slow, /needs stress fast

type of materials most metals (not too cold) /ceramics, ice, cold metals

warning permanent elongation /none

strain energy higher /lower

fractured surface rough/ smoother

necking yes/ no

Ductile Fracture
Stages of ductile fracture
Initial necking
small cavity formation (microvoids)
void growth (elipsoid) by coalescence into a crack
fast crack propagation around neck. Shear strain at 45o
final shear fracture (cup and cone)
The interior surface is fibrous, irregular, which signify plastic deformation.

Brittle Fracture
There is no appreciable deformation, and crack propagation is very fast. In most brittle materials, crack propagation (by bond breaking) is along specific crystallographic planes (cleavage planes). This type of fracture is transgranular (through grains) producing grainy texture (or faceted texture) when cleavage direction changes from grain to grain. In some materials, fracture is intergranular. Principles of Fracture Mechanics

Fracture occurs due to stress concentration at flaws, like surface scratches, voids, etc. If a is the length of the void and r the radius of curvature, the enhanced stress near the flaw is:
sm » 2 s0 (a/r)1/2
where s0 is the applied macroscopic stress. Note that a is 1/2 the length of the flaw, not the full length for an internal flaw, but the full length for a surface flaw. The stress concentration factor is:
Kt = sm/s0 » 2 (a/r)1/2
Because of this enhancement, flaws with small radius of curvature are called stress raisers.

Impact Fracture Testing
Normalized tests, like the Charpy and Izod tests measure the impact energy required to fracture a notched specimen with a hammer mounted on a pendulum. The energy is measured by the change in potential energy (height) of the pendulum. This energy is called notch toughness.
Ductile to brittle transition occurs in materials when the temperature is dropped below a transition temperature. Alloying usually increases the ductile-brittle transition temperature (Fig. 8.19.) For ceramics, this type of transition occurs at much higher temperatures than for metals.

Fatigue
Fatigue is the catastrophic failure due to dynamic (fluctuating) stresses. It can happen in bridges, airplanes, machine components, etc. The characteristics are:
long period of cyclic strain
the most usual (90%) of metallic failures (happens also in ceramics and polymers)
is brittle-like even in ductile metals, with little plastic deformation
it occurs in stages involving the initiation and propagation of cracks.

Cyclic Stresses
These are characterized by maximum, minimum and mean stress, the stress amplitude, and the stress ratio

The S—N Curve
S—N curves (stress-number of cycles to failure) are obtained using apparatus like the one shown in Fig. 8.21. Different types of S—N curves are shown in Fig. 8.22.
Fatigue limit (endurance limit) occurs for some materials (like some ferrous and Ti allows). In this case, the S—N curve becomes horizontal at large N . This means that there is a maximum stress amplitude (the fatigue limit) below which the material never fails, no matter how large the number of cycles is.
For other materials (e.g., non-ferrous) the S—N curve continues to fall with N.
Failure by fatigue shows substantial variability (Fig. 8.23).
Failure at low loads is in the elastic strain regime, requires a large number of cycles (typ. 104 to 105). At high loads (plastic regime), one has low-cycle fatigue (N <>Crack Initiation and Propagation
Stages is fatigue failure:
I. crack initiation at high stress points (stress raisers)
II. propagation (incremental in each cycle)
III. final failure by fracture
Nfinal = Ninitiation + Npropagation
Stage I - propagation
slow
along crystallographic planes of high shear stress
flat and featureless fatigue surface
Stage II - propagation
crack propagates by repetive plastic blunting and sharpening of the crack tip. (Fig. 8.25.)
. Crack Propagation Rate (not covered)
. Factors That Affect Fatigue Life
Mean stress (lower fatigue life with increasing smean).
Surface defects (scratches, sharp transitions and edges). Solution:
polish to remove machining flaws
add residual compressive stress (e.g., by shot peening.)
case harden, by carburizing, nitriding (exposing to appropriate gas at high temperature)
. Environmental Effects
Thermal cycling causes expansion and contraction, hence thermal stress, if component is restrained. Solution:
eliminate restraint by design
use materials with low thermal expansion coefficients.
Corrosion fatigue. Chemical reactions induced pits which act as stress raisers. Corrosion also enhances crack propagation. Solutions:
decrease corrosiveness of medium, if possible.
add protective surface coating.
add residual compressive stresses.

Creep
Creep is the time-varying plastic deformation of a material stressed at high temperatures. Examples: turbine blades, steam generators. Keys are the time dependence of the strain and the high temperature.

. Generalized Creep Behavior

At a constant stress, the strain increases initially fast with time (primary or transient deformation), then increases more slowly in the secondary region at a steady rate (creep rate). Finally the strain increases fast and leads to failure in the tertiary region. Characteristics:
Creep rate: de/dt
Time to failure.
. Stress and Temperature Effects
Creep becomes more pronounced at higher temperatures (Fig. 8.37). There is essentially no creep at temperatures below 40% of the melting point.
Creep increases at higher applied stresses.
The behavior can be characterized by the following expression, where K, n and Qc are constants for a given material:
de/dt = K sn exp(-Qc/RT)
. Data Extrapolation Methods (not covered.)
. Alloys for High-Temperature Use
These are needed for turbines in jet engines, hypersonic airplanes, nuclear reactors, etc. The important factors are a high melting temperature, a high elastic modulus and large grain size (the latter is opposite to what is desirable in low-temperature materials).
Some creep resistant materials are stainless steels, refractory metal alloys (containing elements of high melting point, like Nb, Mo, W, Ta), and superalloys (based on Co, Ni, Fe.)

Chapter 7. DISLOCATIONS AND STRENGTHENING MECHANISM

Introduction
The key idea of the chapter is that plastic deformation is due to the motion of a large number of dislocations. The motion is called slip. Thus, the strength (resistance to deformation) can be improved by putting obstacles to slip.

Basic Concepts
Dislocations can be edge dislocations, screw dislocations and exist in combination of the two (Ch. 4.4). Their motion (slip) occurs by sequential bond breaking and bond reforming (Fig. 7.1). The number of dislocations per unit volume is the dislocation density, in a plane they are measured per unit area.

Characteristics of Dislocations
There is strain around a dislocation which influences how they interact with other dislocations, impurities, etc. There is compression near the extra plane (higher atomic density) and tension following the dislocation line (Fig. 7.4)
Dislocations interact among themselves (Fig. 7.5). When they are in the same plane, they repel if they have the same sign and annihilate if they have opposite signs (leaving behind a perfect crystal). In general, when dislocations are close and their strain fields add to a larger value, they repel, because being close increases the potential energy (it takes energy to strain a region of the material).
The number of dislocations increases dramatically during plastic deformation. Dislocations spawn from existing dislocations, and from defects, grain boundaries and surface irregularities.

Slip Systems
In single crystals there are preferred planes where dislocations move (slip planes). There they do not move in any direction, but in preferred crystallographic directions (slip direction). The set of slip planes and directions constitute slip systems.
The slip planes are those of highest packing density. How do we explain this? Since the distance between atoms is shorter than the average, the distance perpendicular to the plane has to be longer than average. Being relatively far apart, the atoms can move more easily with respect to the atoms of the adjacent plane. (We did not discuss direction and plane nomenclature for slip systems.)
BCC and FCC crystals have more slip systems, that is more ways for dislocation to propagate. Thus, those crystals are more ductile than HCP crystals (HCP crystals are more brittle).

Slip in Single Crystals
A tensile stress s will have components in any plane that is not perpendicular to the stress. These components are resolved shear stresses. Their magnitude depends on orientation (see Fig. 7.7).
tR = s cos f cos l
If the shear stress reaches the critical resolved shear stress tCRSS, slip (plastic deformation) can start. The stress needed is:
sy = tCRSS / (cos f cos l)max
at the angles at which tCRSS is a maximum. The minimum stress needed for yielding is when f = l = 45 degrees: sy = 2tCRSS. Thus, dislocations will occur first at slip planes oriented close to this angle with respect to the applied stress